Question 1
Four colleagues need to schedule a meeting. Their available time slots are:
- Alex: 9:00 AM, 10:00 AM, 2:00 PM, 3:00 PM
- Ben: 10:00 AM, 11:00 AM, 2:00 PM
- Cara: 9:00 AM, 11:00 AM, 12:00 PM, 3:00 PM
- Diana: 10:00 AM, 12:00 PM, 2:00 PM, 3:00 PM
What is the earliest time slot when all four can meet?
Step-by-step solution:
Set Intersection Method:
1. List all availability:
- Alex: {9:00 AM, 10:00 AM, 2:00 PM, 3:00 PM}
- Ben: {10:00 AM, 11:00 AM, 2:00 PM}
- Cara: {9:00 AM, 11:00 AM, 12:00 PM, 3:00 PM}
- Diana: {10:00 AM, 12:00 PM, 2:00 PM, 3:00 PM}
2. Find common slots (intersection):
- Common to all = Alex AND Ben AND Cara AND Diana
- Result: Empty set (No common time)
3. Conclusion: No common time slot available
Key Strategy: Use set intersection to find common availability, then choose the earliest time.
Set Intersection Method:
1. List all availability:
- Alex: {9:00 AM, 10:00 AM, 2:00 PM, 3:00 PM}
- Ben: {10:00 AM, 11:00 AM, 2:00 PM}
- Cara: {9:00 AM, 11:00 AM, 12:00 PM, 3:00 PM}
- Diana: {10:00 AM, 12:00 PM, 2:00 PM, 3:00 PM}
2. Find common slots (intersection):
- Common to all = Alex AND Ben AND Cara AND Diana
- Result: Empty set (No common time)
3. Conclusion: No common time slot available
Key Strategy: Use set intersection to find common availability, then choose the earliest time.